Cyclist coasting down a hill cons. of energy

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In summary, the question asks for the cyclist's power output to climb a 7.0° hill at a steady speed of 5.0m/s, assuming a total mass of 75kg. The equation for power is used to solve for the power output, taking into account the force of friction. The final answer is 448W.
  • #1
totallyclone
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Homework Statement


A bicyclist coasts down a 7.0° hill at a steady speed of 5.0m/s. Assuming a total mass of 75kg (bicycle plus rider), what must be the cyclist's power output to climb the same hill at the same speed?


Homework Equations


EK=1/2 mv2
EG=mgh
P=W/T


The Attempt at a Solution


I tried the question and this is what I got but I'm answer if this is right... not sure if there's a Force of friction though because I read the question and assumed there isn't any force of friction... but I'm unsure... :uhh:

P=W/T
P=-WGΔdcos180°/T
P=-WGvcos180°
P=-mgsin7.0°(5.0)cos180°
P=-(75)(9.8)sin7.0°(5.0)cos180°
P=448W
 
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  • #2
Well if the cyclist goes down the hill with constant speed, then there must be some kind of force that's stopping him from accelerating, so you should account for it accordingly.
 
  • #3
hi totallyclone! :smile:
totallyclone said:
A bicyclist coasts down a 7.0° hill at a steady speed of 5.0m/s. Assuming a total mass of 75kg (bicycle plus rider), what must be the cyclist's power output to climb the same hill at the same speed?
…
not sure if there's a Force of friction …

he couldn't coast (at a steady speed) if there wasn't friction, could he? :wink:
 
  • #4
tiny-tim said:
hi totallyclone! :smile:


he couldn't coast (at a steady speed) if there wasn't friction, could he? :wink:

so...THERE'S FRICTION!?
 
  • #5
yup! :smile:
 

1. How does a cyclist coasting down a hill conserve energy?

When a cyclist is coasting down a hill, gravity is the primary force propelling them forward. This means that the cyclist does not have to use their own energy to pedal, thus conserving their energy.

2. What is potential energy and how does it relate to a cyclist coasting down a hill?

Potential energy is the energy stored in an object due to its position or state. In the case of a cyclist coasting down a hill, the potential energy is converted into kinetic energy as the cyclist gains speed. This kinetic energy then allows the cyclist to continue moving without needing to use their own energy.

3. Does a cyclist coasting down a hill always conserve energy?

In theory, yes, a cyclist coasting down a hill will always conserve energy. However, factors such as air resistance and friction may cause the cyclist to lose some energy, resulting in a slight decrease in speed. Additionally, if the hill is not steep enough or if the cyclist is not in an optimal position, they may need to use some of their own energy to maintain their speed.

4. How does the weight of the cyclist affect their conservation of energy while coasting down a hill?

The weight of the cyclist does not directly affect their conservation of energy while coasting down a hill. However, a heavier cyclist may have more potential energy at the top of the hill, which can then be converted into more kinetic energy while coasting down.

5. Are there any ways for a cyclist to increase their conservation of energy while coasting down a hill?

Yes, there are a few ways a cyclist can increase their conservation of energy while coasting down a hill. These include tucking their body to reduce air resistance, choosing a steeper hill for more potential energy, and maintaining a steady speed to minimize the effects of air resistance and friction.

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